If we make the complex numbers \(t_{o,i}\)  vary as \(t_i\) , but remaining pairwise distinct, the space \(H^1(S^1,_{S^1}^(^))\)  varies in a locally constant way, as we will recall below. Understanding the behaviour of the Stokes matrices in such a variation needs more care, since they depend on the choice of the generic \(\theta _o\in S^1\) , which can become non generic for some values of the parameters \(t_i\) . Apparent real singularities may thus appear in the parameter space. This explains why we will use the language of sheaves of Stokes torsors instead of that of Stokes matrices: we wish to avoid these apparent singularities. However, if we vary \(t_i\)  along a real parameter in such a way that \(\theta _o\)  and the corresponding order can be chosen constant all along the deformation, then the representation in terms of Stokes matrices holds all along the deformation. This includes limit cases where some \(t_i\) 's may coincide: coalescence of eigenvalues occurs in the sense of [1]}.
